Quantifying topological robustness of networks under sustained targeted attacks

In this paper, we introduce a measure to analyse the structural robustness of complex networks, which is specifically applicable in scenarios of targeted, sustained attacks. The measure is based on the changing size of the largest component as the network goes through disintegration. We argue that the measure can be used to quantify and compare the effectiveness of various attack strategies. Applying this measure, we confirm the result that scale-free networks are comparatively less vulnerable to random attacks and more vulnerable to targeted attacks. Then we analyse the robustness of a range of real world networks, and show that most real world networks are least robust to attacks based on betweenness of nodes. We also show that the robustness values of some networks are more sensitive to the attack strategy as compared to others. Furthermore, robustness coefficient computed using two centrality measures may be similar, even when the computational complexities of calculating these centrality measures may be different. Given this disparity, the robustness coefficient introduced potentially plays a key role in choosing attack and defence strategies for real world networks. While the measure is applicable to all types of complex networks, we clearly demonstrate its relevance to social network analysis.

[1]  Tang Xianchao,et al.  Dolphin social network , 2014 .

[2]  Albert Y. Zomaya,et al.  Local assortativeness in scale-free networks , 2008 .

[3]  Albert Y. Zomaya,et al.  Local assortativity and growth of Internet , 2009 .

[4]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[5]  Sandra Orchard,et al.  Molecular interaction databases , 2012, Proteomics.

[6]  Sharon L. Milgram,et al.  The Small World Problem , 1967 .

[7]  Venkat Venkatasubramanian,et al.  Spontaneous emergence of complex optimal networks through evolutionary adaptation , 2004, Comput. Chem. Eng..

[8]  Pablo M. Gleiser,et al.  Community Structure in Jazz , 2003, Adv. Complex Syst..

[9]  W. Zachary,et al.  An Information Flow Model for Conflict and Fission in Small Groups , 1977, Journal of Anthropological Research.

[10]  Mark E. J. Newman.  A measure of betweenness centrality based on random walks , 2005, Soc. Networks.

[11]  Anthony H. Dekker,et al.  Network Robustness and Graph Topology , 2004, ACSC.

[12]  J. Hanley,et al.  The meaning and use of the area under a receiver operating characteristic (ROC) curve. , 1982, Radiology.

[13]  Jan Baumbach,et al.  CoryneRegNet 4.0 – A reference database for corynebacterial gene regulatory networks , 2007, BMC Bioinformatics.

[14]  Bradley S. Rees,et al.  Overlapping community detection using a community optimized graph swarm , 2012, Social Network Analysis and Mining.

[15]  Phillip Bonacich,et al.  Eigenvector-like measures of centrality for asymmetric relations , 2001, Soc. Networks.

[16]  Massimo Marchiori,et al.  Error and attacktolerance of complex network s , 2004 .

[17]  E. Kreyszig,et al.  Advanced Engineering Mathematics. , 1974 .

[18]  Falk Schreiber,et al.  Analysis of Biological Networks (Wiley Series in Bioinformatics) , 2008 .

[19]  Janet Efstathiou,et al.  Structural robustness of complex network , 2006 .

[20]  Shi Zhou,et al.  The rich-club phenomenon in the Internet topology , 2003, IEEE Communications Letters.

[21]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[22]  R. Solé,et al.  Information Theory of Complex Networks: On Evolution and Architectural Constraints , 2004 .

[23]  Heiko Rieger,et al.  Random walks on complex networks. , 2004, Physical review letters.

[24]  L. da F. Costa,et al.  Characterization of complex networks: A survey of measurements , 2005, cond-mat/0505185.

[25]  Olaf Sporns,et al.  Information flow in local cortical networks is not democratic , 2008, BMC Neuroscience.

[26]  Alessandro Vespignani,et al.  Detecting rich-club ordering in complex networks , 2006, physics/0602134.

[27]  Faraz Zaidi,et al.  Communities and hierarchical structures in dynamic social networks: analysis and visualization , 2011, Social Network Analysis and Mining.

[28]  Faraz Zaidi,et al.  Small world networks and clustered small world networks with random connectivity , 2012, Social Network Analysis and Mining.

[29]  Albert-László Barabási,et al.  Evolution of Networks: From Biological Nets to the Internet and WWW , 2004 .

[30]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[31]  Hideaki Takeda,et al.  Using dynamic community detection to identify trends in user-generated content , 2012, Social Network Analysis and Mining.